I-5 and the Physics of Bridge Collapses

I-5 and the Physics of Bridge Collapses
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Another US bridge collapse is in the news. Last week, a large section of the I-5 bridge over the Skagit River in Washington State crumbled and crashed into the river below. Thankfully, no one died and the survivors are not seriously injured.

The collision of a large truck with a structural beam seems to have set off the disaster, but full analysis of the event is not complete. Further engineering investigations over the coming weeks and months will likely find a precise chain of causes that led to the collapse.

Investigators will follow a path dictated by the applied science of bridge design. The same physical principles underlying a bridge's design also prepossess it to fail in particular ways.

Individual bridges are mostly variations on a handful of canonical base designs. Smaller crossings, requiring less than roughly 100 feet of clearance and allowing closely spaced supports, often employ a basic girder design: concrete beams lying atop concrete pillars. They rarely fail. Their designs are less demanding and many are newer, as girder bridge use has expanded as reinforced concrete technology has improved.

Taller bridges with fewer supports, however, are usually constructed according to truss, suspension, or cantilever designs, each of which is susceptible to particular modes of failure.

Truss Bridges

Truss structures, like the I-5 bridge, are composed of steel beams in the shape of triangles. Why triangles? Because they're the strongest geometric shape. Three beams arranged in a triangle, meeting at three corners, cannot shift position without a corner coming apart. Shapes such as squares and pentagons can change shape without the joints being broken. (Try this yourself with toothpicks or pencils.) A truss bridge holds as long as the beams themselves don't break and the joints stay together.

Most truss collapses are either traced back to a corner failing or a beam breaking. The famous 2007 collapse of the I-35 bridge over the Mississippi River in Minnesota was due to a triangle corner failing. A steel brace plate (known as a gusset) that held a corner in place warped and bowed out, eventually cracking and breaking.

When an enormous truck hit the Skagit River bridge, it likely bent one of the triangle beams near the top of the truss structure. Once this beam bent or broke, the corners were no longer held in place. An educated guess as to the cause of the disaster would be a chain reaction of collapsing truss triangles triggered by the single broken beam. A single beam eliciting a complete failure, however, may suggest that further weaknesses existed in the bridge.

Suspension Bridges

Suspension bridges are the graceful giant icons that come to mind when we think of bridges: The Golden Gate Bridge, the Brooklyn Bridge, the Sydney Harbour Bridge. Lofty towers anchor them along their routes. Cables run from tower to tower along the direction of the bridge. From these massive cables, smaller ones hang straight down and attach to the road deck on its sides. (Think of how the seat of a swing is supported by chains.) The road deck is not rigidly anchored in place like in a truss structure but may sway a bit. 

Suspension bridge collapses are usually due to vibrations in the bridge hitting what is called resonance. "Resonant frequency" is a property of all objects; when an external force causes the bridge to vibrate at its resonant frequency, it causes the vibration to grow stronger and stronger. This phenomenon is widely thought to have caused the famous 1940 Tacoma Narrows Bridge collapse, but the collapse should be more precisely blamed on aerostatic flutter.* (Apparently, Washington State isn't good at building bridges.) An actual example was Angers Bridge in France. An army marching in unison caused the bridge to vibrate and collpase.

Cantilever Bridges

Cantilever bridges look precarious at first glance because their spans spread horizontally from a small base with no other support, like giant levers. These bridges, when built with the latest steel technology, can support single spans nearly a mile long with no supports beneath. They also require no temporary supports during construction, which greatly reduces cost.

Failure of a cantilever bridge is usually due to construction errors or miscalculation of just how much torque the lever arm can take. They may also collapse if a ship strikes a crucial support.

The Trouble with Bridges

Knowing the problems to which a particular structure is susceptible is crucial to diagnosing the cause of its unexpected demise. Weaknesses are inherent to every design.

For the I-5 truss bridge, the compromise of a structural triangle was likely fatal. The impact of an over-sized truck triggered the collapse; whether that impact was beyond the design of the bridge to withstand, or the bridge was already failing due to age or a particular design flaw, will be determined by engineers in the coming months.

*Note: "Aeroelastic flutter" is indeed a type of resonance phenomenon, a vibration with a preferred frequency at which it settles and becomes self-amplifying.

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